PhD Chapter 3
Results 1/3
This series of files compile all analyses done during Chapter 3:
- Section 1 presents the calculation of the indices of exposure.
- Section 2 presents variable exploration and regressions results.
- Section 3 presents species distribution models.
All analyses have been done with R 4.0.2.
Click on the table of contents in the left margin to assess a specific analysis.
Click on a figure to zoom it
Sources of activity considered for the analyses:
- aquaculture: mussel farm (AquaInf)
- city: general diffusive influence, wharves (CityInf, CityWha)
- industry: general diffusive influence, wharves (Indu, InduWha)
- sediment dredging: collection zones, dumping zones (DredColl, DredDump)
- commercial shipping: mooring sites, traffic routes (ShipMoor, ShipTraf)
- sewers: rainwater drains, wastewater drains (SewRain, SewWast)
Fisheries data considered for the analyses (expressed as number of fishing events or kilograms of collected individuals for each gear):
| Gear | Code | Years | Events | Species |
|---|---|---|---|---|
| Dredge | FishDred | 2010-2014 | 21 | Mactromeris polynyma |
| Net | FishNet | 2010 | 5 | Clupea harengus, Gadus morhua |
| Trap | FishTrap | 2010-2015 | 1061 | Buccinum sp., Cancer irroratus, Chionoecetes opilio, Homarus americanus |
| Bottom-trawl | FishTraw | 2013-2014 | 2 | Pandalus borealis |
1. Maps
1.1. General map
1.2. Parameters maps
Maps of abiotic habitat variables:
Depth
Slope
River CDOM
2. Modelling the influence of human activities
We computed an exposure index for each human activity, which we will use for regression models and SDM (see section 2). Two categories of exposure index were calculated seperately: one for land- and sea-based activities and one for fisheries. These indices are relative, with a variation between 0 (low exposure) to 1 (high exposure).
A cumulative exposure index has been calculated by adding index of exposure of each activity.
2.1. Individual indices of exposure
2.1.1. Land- and sea-based activities
The following map present the sources of land- and sea-based human activities considered here. For each activity, we calculated an index of exposure \(E_{ij}\).
Methodology
To calculate the exposure index \(E_{ij}\), we modelled the diffusion of theoretical particles in an ecosystem. Particles are the resultant of an activity, such as contaminants or sediment, and they diffuse from the source of the activity. Three types of particles have been considered, in order to use multiple sinking rates. Combination of the responses for each particle type will allow to represent each activity by a unique signature.
We simulated the dispersion of these particles using the minimal distance from the source \(D\) and an inverse logarithm relationship, to account for a ‘journey’ in a 2D environment while reducing the contribution of highest values.
The three types of particle considered were:
- slow-sinking particles (< 4 µm): e.g. clay, dissolved organic matter, small bacteria, viruses, chemical components, proteins
- medium-sinking particles (between 4 µm and 2 mm): e.g. sand, silt, small particulate organic matter, large bacteria, phytoplankton, zooplankton
- fast-sinking particles (> 2 mm): e.g. gravel, large particulate organic matter, clusters of dead organisms, large zooplankton, larger organisms
\(D_{ijk}\) has been calculated with least-cost pathfinding methods from the package gdistance. To compute the trajectory of each particles type, we first established a connectivity model based on a ‘resistance seascape’ concept. We created a 100 x 100 m raster in our study area, whose cell can be selected to obtain the path connecting start (source of the activity) and end (raster cell) points. Journey between two neighbour cells (chess queen configuration) has a cost to be included in this path, which is defined on several constraints to account for specific behaviour. The length of the final path then gives the distance.
We considered four underlying principles for the physical constraints:
- marine ecosystems: particles cannot disperse on land
- gravity: particles disperse easily from shallow to deeper depths while the reverse is difficult
- sedimentation: particles cannot disperse anymore when they have sedimented
- hydrodynamism: particles disperse according to local hydrodynamical currents
⚠️ For now, the forth constraint is not yet implemented.
The connectivity model thus considered: (i) coasts as boundaries delimitating cells unselectable by the algorithm, (ii) bathymetry, (iii) a sedimentation distance where cells beyons are unselectable, (iv) river plumes as hydrodynamical fronts with an intensity and a direction (a complete circulation model in BSI is not yet available). These constraints were included in the minimal distance calculation with the transition function \(f_{j}\) used by costDistance() when creating the least-cost path, and the cutoff sedimentation threshold.
- land is set with a connectivity of 0
- bathymetry is compared between two cells:
- when point A is shallower than point B, connectivity is high
- when point A is deeper than point B, connectivity is low (with a certain diffusion)
- cells beyond the cutoff threshold are set with a connectivity of 0
- CDOM content (proxy of hydrodynamism) is compared between two cells (NOT IMPLEMENTED YET)
Values of the parameters used for bathymetry and hydrodynamism contraints depend on the types of particle:
- slow-sinking particles: influenced primarily by hydrodynamics and diffusing over extended areas; gravity eventually sinks them; easily resuspended
- medium-sinking particles: particles both sinking due to gravity and spreading by hydrodynamic influence, resuspension possible but difficult
- fast-sinking particles: dense aggregates that sink easily due to gravity and are unaffected by hydrodynamical effects; resuspension is highly difficult
This resulted in the following transition functions \(f_{j}\) and cutoff thresholds \(T_{k}\) (in meters):
| Transition function | |
|---|---|
| slow | ifelse(bathy[1] > bathy[2], (1 - ((bathy[2] - bathy[1]) / bathy[2])), 0.9) |
| medium | ifelse(bathy[1] > bathy[2], (1 - ((bathy[2] - bathy[1]) / bathy[2])), 0.45) |
| fast | ifelse(bathy[1] > bathy[2], (1 - ((bathy[2] - bathy[1]) / bathy[2])), 0.1) |
| slow | medium | fast | |
|---|---|---|---|
| cutoff | 7500 | 3500 | 500 |
⚠️ These values need to be groundtruthed by litterature research and expert opinion.
The equation for \(D_{ijk}\) is then:
\[ \left\{\begin{matrix} D_{ijk} = f_{k} \left( B_{i}, H_{i} \right) & D_{ij} < T_{k} \\ D_{ijk} = 0 & D_{ijk} > T_{k} \end{matrix}\right. \]
- \(f_{k}\) is the transition function
- \(B_{i}\) is the bathymetry component
- \(H_{i}\) is the hydrodynamics component
- \(T_{k}\) is the cutoff distance
- \(i\) is a cell
- \(j\) is a human activity
- \(k\) is the particle type (slow-, medium-, fast-sinking)
This allowed to calculate \(L_{ijk}\) with the inverse logarithm relationship (plus one to avoid infinite values).
\[ L^{'}_{ijk} = \frac{1}{ln(D_{ijk} + 1)} \]
\(L^{'}_{ijk}\) was standardized to vary within a scale between 0 and 1, with \(min(L^{'}_{ijk})\) and \(max(L^{'}_{ijk})\), to get \(L_{ijk}\).
Finally, the exposure index \(E_{ij}\) was computed by combining each \(L_{ijk}\) in a weighted sum using coefficients \(p_{jk}\), initialized as such:
| AquaInf | CityInf | CityWha | DredColl | DredDump | InduInf | InduWha | SewRain | SewWast | ShipMoor | ShipTraf | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| small | 0.6 | 0.6 | 0.4 | 0.1 | 0.1 | 0.7 | 0.4 | 0.5 | 0.4 | 0.4 | 0.4 |
| medium | 0.3 | 0.3 | 0.4 | 0.3 | 0.3 | 0.2 | 0.4 | 0.4 | 0.5 | 0.4 | 0.4 |
| large | 0.1 | 0.1 | 0.2 | 0.6 | 0.6 | 0.1 | 0.2 | 0.1 | 0.1 | 0.2 | 0.2 |
⚠️ These values need to be groundtruthed by litterature research and expert opinion.
\[ E^{'}_{ij} = \sum_{k}^{s,m,l} \Big( L_{ijk} . p_{jk} \Big) \]
- \(L_{ijk}\) is the standardised minimal distance from the source of activity for each particle type
- \(p_{jk}\) is the proportion of each type of particle
- \(i\) is a cell
- \(j\) is a human activity
- \(k\) is the particle type (slow-, medium-, fast-sinking)
Likewise, \(E^{'}_{ij}\) was standardized to vary within a scale between 0 and 1, with \(min(E^{'}_{ij})\) and \(max(E^{'}_{ij})\), to get \(E_{ij}\).
Results
The following maps present the values of \(E_{ij}\) for land/sea-based activities (grey = low exposure; dark blue = high exposure).
Aquaculture
City
Dredging
Industry
Sewers
Shipping
2.1.2. Fisheries
These data belong to Department of Fisheries and Oceans Canada, with a permission granted to David Beauchesne. As such, we cannot present raw products and we will work on derived data.
Here, \(E_{ij}\) have been calculated with a proxy based on fisheries data for each gear used in the area.
Methodology
We extracted data from a global database for the St. Lawrence, for all fishing events occuring within the Baie des Sept-Îles. Four types of gears (traps, bottom-trawls, nets and dredges) have been considered in the bay between 2010 and 2015. Eight species have been gathered (see table at the top of this page).
As each gear was not used consistently during this period, we averaged the number of fishing events to obtain a proxy of fishing intensity. Furthermore, we modified this proxy with a smoothing function in order to ‘diffuse’ the signal around the actual event.
Results
The following maps present the values of \(E_{ij}\) for fisheries (grey = low exposure; dark blue = high exposure).
Dredge
Net
Trap
Bottom-trawling
2.2. Cumulative exposure index
Here, we combine individual exposure indices into a unique value, the cumulative exposure index \(CE_{i}\), here with an additive relationship:
\[ CE_{i} = \sum_{j} E_{ij} \]
In future iterations, we will try different link functions to account for non-additive effects. This score varies between 0 and 10 (total number of considered human activities).
The cumulative exposure index has been represented in five classes, according to the colour code of the Marine Strategy Framework Directive (indigo = bad exposure, less than 20 %; crimson = high exposure, higher than 80 %).
This histogram represents the number of stations falling in each class:
These scores will be used for the species distribution models (see Section 3).